12.7 Suppose, as in Problem 12.6, a firm produces hockey sticks with a production function of q
2KL. Capital stock is fixed at K in the short run.

a. Calculate the firm’s total costs as a function of q, w, v, and K.

b. Given q, w, and v, how should the capital stock be chosen to minimize total cost?

c. Use your results from part

(b) to calculate the long-run total cost of hockey stick production.

d. For w
$4, v
$1, graph the long-run total cost curve for hockey stick production.

Show that this is an envelope for the short-run curves computed in part

(a) by examining values of K of 100, 200, and 400.